Some ∗-Clean Group Rings-Reference-Cited by-同舟云学术

Some ∗-Clean Group Rings

Published:2015-01-07 Issue:01 Volume:22 Page:169-180
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Gao Yanyan¹²,Chen Jianlong¹,Li Yuanlin³

Affiliation:

1. Department of Mathematics, Southeast University, Nanjing 210096, China

2. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, China

3. Department of Mathematics, Brock University, St. Catharines, L2S 3A1, Canada

Abstract

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection. It is obvious that ∗-clean rings are clean. Vaš asked whether there exists a clean ring with involution that is not ∗-clean. In this paper, we investigate when a group ring RG is ∗-clean, where ∗ is the classical involution on RG. We obtain necessary and sufficient conditions for RG to be ∗-clean, where R is a commutative local ring and G is one of the groups C3, C4, S3 and Q8. As a consequence, we provide many examples of group rings which are clean but not ∗-clean.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386715000152

Reference10 articles.

1. Group rings in which every element is uniquely the sum of a unit and an idempotent

2. Rings in which elements are uniquely the sum of an idempotent and a unit that commute

3. EXTENSIONS OF CLEAN RINGS

4. ON STRONGLY *-CLEAN RINGS

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